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Concept of inequality

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Concept of inequality

by shrutib » Thu May 31, 2012 7:44 am
Can someone just explain me the concept of inequality and finding range... Both finite and disjoint.

Moreover, i would like to know the things i should remember so that i can solve almost all the problems(specially in D.S. area) in inequalities involving these concepts.


Thank you.
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by mathbyvemuri » Thu May 31, 2012 8:08 am
One concept on inequality:
This one is finding the range of variable x when an inequality with quadratic expression is given:
If (x-a)(x-b)>0,
then x<a and x>b for a<b
or x<b and x>a for a>b


If (x-a)(x-b)<0,
then a<x<b for a<b
or b<x<a for a>b

getting the quadratic form into (x-a)(x-b) is the key here. This is nothing but factorisation.
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by GMAT Kolaveri » Thu May 31, 2012 8:55 am
1. Only linear equations in x (degree of x is 1) have unique solution for x.
non-linear equations (x^2,x^3) have more than one solution.

2. |x| < a implies -a < x < a

3. Do not assume any variable to be an integer unless it is explicitly stated in the question.

4. Use extreme values when testing the statements with numbers.
suppose x < 2. we can test with x =1.9999
X < 3.45, we can use X = 3.4444

5. When X is mentioned as integer, always test with 0

6. align inequalities having the same sign so that they can be visually compared.

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